House Prices, Credit Growth, and Excess Volatility: Implications for Monetary and Macroprudential Policy pptx

Specifically, we show that theintroduction of simple moving-average forecast rules for a subset of households can signif-icantly magnify the volatility and persistence of house prices an

FEDERAL RESERVE BANK OF SAN FRANCISCO

WORKING PAPER SERIES

House Prices, Credit Growth, and Excess Volatility:

Implications for Monetary and Macroprudential Policy

Paolo Gelain Norges Bank

Kevin J Lansing Federal Reserve Bank of San Francisco and Norges Bank

Caterina Mendicino Bank of Portugal

August 2012

The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the Board of Governors of the Federal Reserve System

Working Paper 2012-11

http://www.frbsf.org/publications/economics/papers/2012/wp12-11bk.pdf

House Prices, Credit Growth, and Excess Volatility:

Implications for Monetary and Macroprudential Policy ∗

Paolo Gelain†

Norges Bank

Kevin J Lansing‡FRB San Francisco and Norges Bank

Caterina Mendicino§Bank of Portugal August 10, 2012

AbstractProgress on the question of whether policymakers should respond directly to financialvariables requires a realistic economic model that captures the links between asset prices,credit expansion, and real economic activity Standard DSGE models with fully-rationalexpectations have difficulty producing large swings in house prices and household debt thatresemble the patterns observed in many developed countries over the past decade We in-troduce excess volatility into an otherwise standard DSGE model by allowing a fraction

of households to depart from fully-rational expectations Specifically, we show that theintroduction of simple moving-average forecast rules for a subset of households can signif-icantly magnify the volatility and persistence of house prices and household debt relative

to otherwise similar model with fully-rational expectations We evaluate various policyactions that might be used to dampen the resulting excess volatility, including a directresponse to house price growth or credit growth in the central bank’s interest rate rule,the imposition of more restrictive loan-to-value ratios, and the use of a modified collateralconstraint that takes into account the borrower’s loan-to-income ratio Of these, we findthat a loan-to-income constraint is the most effective tool for dampening overall excessvolatility in the model economy We find that while an interest-rate response to houseprice growth or credit growth can stabilize some economic variables, it can significantlymagnify the volatility of others, particularly inflation

Keywords: Asset Pricing, Excess Volatility, Credit Cycles, Housing Bubbles, Monetarypolicy, Macroprudential policy

JEL Classification: E32, E44, G12, O40

∗ This paper has been prepared for presentation at the Fourth Annual Fall Conference of the International Journal of Central Banking hosted by the Central Bank of Chile, September 27-28, 2012 For helpful comments and suggestions, we would like to thank Kjetil Olsen, Øistein Røisland, Anders Vredin, seminar participants at the Norges Bank Macro-Finance Forum, the 2012 Meeting of the International Finance and Banking Society, and the 2012 Meeting of the Society for Computational Economics.

† Norges Bank, P.O Box 1179, Sentrum, 0107 Oslo, email: paolo.gelain@norges-bank.no

‡ Corresponding author Federal Reserve Bank of San Francisco, P.O Box 7702, San Francisco, CA

94120-7702, email: kevin.j.lansing@sf.frb.org or kevin.lansing@norges-bank.no

§ Bank of Portugal, Department of Economic Studies, email: cmendicino@bportugal.pt

1 Introduction

Household leverage in many industrial countries increased dramatically in the years prior to

2007 Countries with the largest increases in household debt relative to income tended toexperience the fastest run-ups in house prices over the same period The same countriestended to experience the most severe declines in consumption once house prices started falling

house prices during the boom years of the mid-2000s rose faster in areas where subprime andexotic mortgages were more prevalent (Mian and Sufi 2009, Pavlov and Wachter 2011) In

a given area, past house price appreciation had a significant positive influence on subsequentloan approval rates (Goetzmann et al 2012) Areas which experienced the largest run-ups

in household leverage tended to experience the most severe recessions as measured by thesubsequent fall in durables consumption or the subsequent rise in the unemployment rate(Mian and Sufi 2010) Overall, the data suggests the presence of a self-reinforcing feedbackloop in which an influx of new homebuyers with access to easy mortgage credit helped fuel

an excessive run-up in house prices The run-up, in turn, encouraged lenders to ease creditfurther on the assumption that house prices would continue to rise Recession severity in agiven area appears to reflect the degree to which prior growth in that area was driven by anunsustainable borrowing trend–one which came to an abrupt halt once house prices stoppedrising (Mian and Sufi 2012)

Figure 1 illustrates the simultaneous boom in U.S real house prices and per capita realhousehold debt that occurred during the mid-2000s During the boom years, per capita realGDP remained consistently above trend At the time, many economists and policymakersargued that the strength of the U.S economy was a fundamental factor supporting houseprices However, it is now clear that much of the strength of the economy during this time waslinked to the housing boom itself Consumers extracted equity from appreciating home values

to pay for all kinds of goods and services while hundreds of thousands of jobs were created

in residential construction, mortgage banking, and real estate After peaking in 2006, realhouse prices have retraced to the downside while the level of real household debt has started

to decline Real GDP experienced a sharp drop during the Great Recession and remains about5% below trend Other macroeconomic variables also suffered severe declines, including per

The unwinding of excess household leverage via higher saving or increased defaults is

1

King (1994) identified a similar correlation between prior increases in household leverage and the severity

of the early 1990s recession using data for ten major industrial countries from 1984 to 1992 He also notes that U.S consumer debt more than doubled during the 1920s–a factor that likely contributed to the severity of the Great Depression in the early 1930s.

2

For details, see Lansing (2011).

imposing a significant drag on consumer spending and bank lending in many countries, thus

crisis and the Great Recession, it is important to consider what lessons might be learned forthe conduct of policy Historical episodes of sustained rapid credit expansion together withbooming stock or house prices have often signaled threats to financial and economic stability(Borio and Lowe 2002) Times of prosperity which are fueled by easy credit and rising debtare typically followed by lengthy periods of deleveraging and subdued growth in GDP andemployment (Reinhart and Reinhart 2010) According to Borio and Lowe (2002) “If theeconomy is indeed robust and the boom is sustainable, actions by the authorities to restrainthe boom are unlikely to derail it altogether By contrast, failure to act could have much moredamaging consequences, as the imbalances unravel.” This point raises the question of what

“actions by authorities” could be used to restrain the boom? Our goal in this paper is toexplore the effects of various policy measures that might be used to lean against credit-fueledfinancial imbalances

Standard DSGE models with fully-rational expectations have difficulty producing largeswings in house prices and household debt that resemble the patterns observed in many devel-oped countries over the past decade Indeed, it is common for such models to include highlypersistent exogenous shocks to rational agents’ preferences for housing in an effort to bridge

preference shocks, then central banks would seem to have little reason to be concerned aboutthem Declines in the collateral value of an asset are often modeled as being driven by exoge-nous fundamental shocks to the “quality” of the asset, rather than the result of a burst asset

models are (to my taste) patently unrealistic I believe that [macroeconomists] are ping themselves by only looking at shocks to fundamentals like preferences and technology.Phenomena like credit market crunches or asset market bubbles rely on self-fulfilling beliefsabout what others will do.” These ideas motivate consideration of a model where agents’subjective forecasts serve as an endogenous source of volatility

handicap-We use the term “excess volatility” to describe a situation where macroeconomic variablesmove too much to be explained by a rational response to fundamentals Numerous empiricalstudies starting with Shiller (1981) and LeRoy and Porter (1981) have shown that stock prices

3 See, for example, Roxburgh, et al (2012).

appear to exhibit excess volatility when compared to the discounted stream of ex post realized

ratios cannot be fully explained by movements in future rent growth

We introduce excess volatility into an otherwise standard DSGE model by allowing afraction of households to depart from fully-rational expectations Specifically, we show thatthe introduction of simple moving-average forecast rules, i.e., adaptive expectations, for asubset of households can significantly magnify the volatility and persistence of house pricesand household debt relative to otherwise similar model with fully-rational expectations Asshown originally by Muth (1960), a moving-average forecast rule with exponentially-decliningweights on past data will coincide with rational expectations when the forecast variable evolves

as a random walk with permanent and temporary shocks Such a forecast rule can be viewed asboundedly-rational because it economizes on the costs of collecting and processing information

As noted by Nerlove (1983, p 1255): “Purposeful economic agents have incentives to eliminateerrors up to a point justified by the costs of obtaining the information necessary to do so Themost readily available and least costly information about the future value of a variable is its

The basic structure of the model is similar to Iacoviello (2005) with two types of holds Patient-lender households own the entire capital stock and operate monopolistically-competitive firms Impatient-borrower households derive income only from labor and face

house-a borrowing constrhouse-aint linked to the mhouse-arket vhouse-alue of their housing stock Expecthouse-ations house-aremodeled as a weighted-average of a fully-rational forecast rule and a moving-average forecastrule We calibrate the parameters of the hybrid expectations model to generate an empiricallyplausible degree of volatility in the simulated house price and household debt series Our setupimplies that 30% of households employ a moving-average forecast rule while the remaining 70%

the unit root assumption embedded in the moving-average forecast rule serves to magnify thevolatility of endogenous variables in the model Our setup captures the idea that much of therun-up in U.S house prices and credit during the boom years was linked to the influx of an

be more likely to employ simple forecast rules about future house prices, income, etc

6

Lansing and LeRoy (2012) provide a recent update on this literature.

7 An empirical study by Chow (1989) finds that an asset pricing model with adaptive expectations forms one with rational expectations in accounting for observed movements in U.S stock prices and interest rates.

outper-8 Using U.S data over the period 1981 to 2006, Levin et al (2012) estimate that around 65 to 80 percent

of agents employ moving-average forecast rules in the context of DSGE model which omits house prices and household debt.

9

See Mian and Sufi (2009) and Chapter 6 of the report of the U.S Financial Crisis Inquiry Commission (2011), titled “Credit Expansion.”

Figure 2 shows that house price forecasts derived from the futures market for the Shiller house price index (which are only available from 2006 onwards) often exhibit a series

Case-of one-sided forecast errors The futures market tends to overpredict future house prices whenprices are falling–a pattern that is consistent with a moving-average forecast rule Similarly,Figure 3 shows that U.S inflation expectations derived from the Survey of Professional Fore-casters tend to systematically underpredict subsequent actual inflation in the sample periodprior to 1979 when inflation was rising and systematically overpredict it thereafter when in-flation was falling Rational expectations would not give rise to such a sustained sequence of

The volatilities of house prices and household debt in the hybrid expectations model areabout two times larger than those in the rational expectations model Both variables exhibithigher persistence under hybrid expectations Stock price volatility is magnified by a factor

of about 1.3, whereas the volatilities of output, labor hours, inflation, and consumption aremagnified by factors ranging from 1.1 to 1.9 These results are striking given that only 30%

of households in the model employ moving-average forecast rules The use of moving-averageforecast rules by even a small subset of agents can have a large influence on model dynamicsbecause the presence of these agents also influences the nature of the fully-rational forecastrules employed by the remaining agents

Given the presence of excess volatility, we evaluate various policy actions that might beused to dampen the observed fluctuations With regard to monetary policy, we consider adirect response to either house price growth or credit growth in the central bank’s interest raterule With regard to macroprudential policy, we consider the imposition of a more restrictiveloan-to-value ratio (i.e., a tightening of lending standards) and the use of a modified collateralconstraint that takes into account the borrower’s loan-to-income ratio Of these, we find that

a loan-to-income constraint is the most effective tool for dampening overall excess volatility

in the model economy We find that while an interest-rate response to house price growth orcredit growth can stabilize some economic variables, it can significantly magnify the volatility

of others, particularly inflation

Our results for an interest rate response to house price growth show some benefits underrational expectations (lower volatilities for household debt and consumption) but the benefitsunder hybrid expectations are less pronounced Under both expectation regimes, inflationvolatility is magnified with the effect being particularly severe under hybrid expectations.Such results are unsatisfactory from the standpoint of an inflation-targeting central bank thatseeks to minimize a weighted-sum of squared deviations of inflation and output from target

1 0

Numerous studies document evidence of bias and inefficiency in survey forecasts of U.S inflation See, for example, Roberts (1997), Mehra (2002), Carroll (2003), and Mankiw, Reis, and Wolfers (2004) More recently, Coibion and Gorodnichencko (2012) find robust evidence against full-information rational expectations in survey forecasts for U.S inflation and unemployment.

values Indeed we show that the value of a typical central bank loss function rises monotonically

as more weight in placed on house price growth in the interest rate rule

The results for an interest rate response to credit growth also show some benefits underrational expectations However, these benefits mostly disappear under hybrid expectations

results for this experiment demonstrate that the effects of a particular monetary policy can be

that a strong interest-rate response to credit growth can improve the welfare of a representativehousehold in a rational expectations model with news shocks Such results could be sensitive

to their assumption of fully-rational expectations

Turning to macroprudential policy, we find that a reduction in the loan-to-value ratiofrom 0.7 to 0.5 substantially reduces the volatility of household debt under both expectationsregimes, but the volatility of most other variables are slightly magnified by factors rangingfrom 1.01 to 1.08 The volatility of aggregate consumption and aggregate labor hours arelittle changed For policymakers, these mixed stabilization results must be weighed againstthe drawbacks of permanently restricting household access to borrowed money which helpsimpatient households smooth their consumption In the sensitivity analysis, we find that anincrease in the loan-to-value ratio (implying looser lending standards) reduces the volatility ofaggregate consumption and aggregate labor hours but it significantly magnifies the volatility

of household debt A natural alternative to a permanent change in the loan-to-value ratio is toshift the ratio in a countercyclical manner without changing its steady-state value A number

of papers have identified stabilization benefits from the use of countercyclical loan-to-value

Our final policy experiment achieves a countercyclical loan-to-value ratio in a novel way byrequiring lenders to place a substantial weight on the borrower’s wage income in the borrowingconstraint As the weight on the borrower’s wage income increases, the generalized borrowingconstraint takes on more of the characteristics of a loan-to-income constraint Intuitively, aloan-to-income constraint represents a more prudent lending criterion than a loan-to-valueconstraint because income, unlike asset value, is less subject to distortions from bubble-likemovements in asset prices Figure 4 shows that during the U.S housing boom of the mid-2000s,loan-to-value measures did not signal any significant increase in household leverage becausethe value of housing assets rose together with liabilities Only after the collapse of house pricesdid the loan-to-value measures provide an indication of excessive household leverage But by

1 1

Orphanides and Williams (2009) make a related point They find that an optimal control policy derived under the assumption of perfect knowledge about the structure of the economy can perform poorly when knowledge is imperfect.

1 2 See, for example, Kannan, Rabanal and Scott (2009), Angelini, Neri, and Panetta (2010), Christensen and Meh (2011), and Lambertini, Mendicino and Punzi (2011).

then, the over-accumulation of household debt had already occurred.13 By contrast, the ratio

of U.S household debt to disposable personal income started to rise rapidly about five yearsearlier, providing regulators with a more timely warning of a potentially dangerous buildup ofhousehold leverage

We show that the generalized borrowing constraint serves as an “automatic stabilizer” byinducing an endogenously countercyclical loan-to-value ratio In our view, it is much easier andmore realistic for regulators to simply mandate a substantial emphasis on the borrowers’ wageincome in the lending decision than to expect regulators to frequently adjust the maximum

For the generalized borrowing constraint, we impose a weight of 50% on the borrower’s wageincome with the remaining 50% on the expected value of housing collateral The multiplicativeparameter in the borrowing constraint is adjusted to maintain the same steady-state loan-tovalue ratio as in the baseline model Under hybrid expectations, the generalized borrowingconstraint substantially reduces the volatility of household debt, while mildly reducing thevolatility of other key variables, including output, labor hours, inflation, and consumption.Notably, the policy avoids the large undesirable magnification of inflation volatility that isobserved in the two interest rate policy experiments

Comparing across the various policy experiments, the generalized borrowing constraintappears to be the most effective tool for dampening overall excess volatility in the modeleconomy The value of a typical central bank loss function declines monotonically (albeitslightly) as more weight is placed on the borrower’s wage income in the borrowing constraint.The beneficial stabilization results of this policy become more dramatic if the loss function isexpanded to take into account the variance of household debt The expanded loss functioncan be interpreted as reflecting a concern for financial stability Specifically, the variance ofhousehold debt captures the idea that historical episodes of sustained rapid credit expansion

Economic and Policy Reform (2011) has called for central banks to go beyond their tional emphasis on flexible inflation targeting and adopt an explicit goal of financial stability.Similarly, Woodford (2011) argues for an expanded central bank loss function that reflects aconcern for financial stability In his model, this concern is linked to a variable that measuresfinancial sector leverage

tradi-1 3 In a speech in February 2004, Fed Chairman Alan Greenspan remarked “Overall, the household sector seems to be in good shape, and much of the apparent increase in the household sector’s debt ratios over the past decade reflects factors that do not suggest increasing household financial stress.”

1 4 Drehmann et al (2012) employ various methods for distinguishing the business cycle from the financial or credit cycle They argue that the financial cycle is much longer than the traditional business cycle.

1 5 Akram and Eitrheim (2008) investigate different ways of representing a concern for financial stability in a reduced-form econometric model Among other metrics, they consider the standard deviation of the debt-to- income ratio and the standard deviation of the debt service-to-income ratio.

1.1 Related Literature

An important unsettled question in economics is whether policymakers should take deliberate

extraor-dinarily costly when accompanied by significant increases in borrowing On this point, IrvingFisher (1930, p 341) famously remarked, “[O]ver-investment and over-speculation are oftenimportant, but they would have far less serious results were they not conducted with borrowedmoney.” Unlike stocks, the typical residential housing transaction is financed almost entirelywith borrowed money The use of leverage magnifies the contractionary impact of a decline

in asset prices In a study of 21 advanced economies from 1970 to 2008, the InternationalMonetary Fund (2009) found that housing-bust recessions tend to be longer and more severethan stock-bust recessions

Early contributions to the literature on monetary policy and asset prices (Bernanke andGertler 2001, Cecchetti, al 2002) employed models in which bubbles were wholly exogenous,i.e., bubbles randomly inflate and contract regardless of any central bank action Consequently,these models cannot not address the important questions of whether a central bank shouldtake deliberate steps to prevent bubbles from forming or whether a central bank should try todeflate a bubble once it has formed In an effort to address these shortcomings, Filardo (2008)develops a model where the central bank’s interest rate policy can influence the transitionprobability of a stochastic bubble He finds that the optimal interest rate policy includes aresponse to asset price growth

Dupor (2005) considers the policy implications of non-fundamental asset price movementswhich are driven by exogenous “expectation shocks.” He finds that optimal monetary policyshould lean against non-fundamental asset price movements Gilchrist and Saito (2008) findthat an interest-rate response to asset price growth is helpful in stabilizing an economy withrational learning about unobserved shifts in the economy’s stochastic growth trend Airaudo et

al (2012) find that an interest-rate response to stock prices can stabilize an economy againstsunspot shocks in a rational expectations model with multiple equilibria Our analysis differsfrom these papers in that we allow a subset agents to depart from fully-rational expectations

We find that the nature of agents’ expectations can influence the benefits of an interest raterule that responds to house price growth or credit growth

Some recent research that incorporates moving-average forecast rules or adaptive tations into otherwise standard models include Sargent (1999, Chapter 6), Lettau and VanZandt (2003), Evans and Ramey (2006), Lansing (2009), and Huang et al (2009), amongothers Lansing (2009) shows that survey-based measures of U.S inflation expectations arewell-captured by a moving average of past realized inflation rates Huang et al (2009) con-

expec-1 6 For an overview of the various arguments, see Lansing (2008).

clude that “adaptive expectations can be an important source of frictions that amplify andpropagate technology shocks and seem promising for generating plausible labor market dy-namics.”

Constant-gain learning algorithms of the type described by Evans and Honkapoja (2001)are similar in many respects to adaptive expectations; both formulations assume that agentsapply exponentially-declining weights to past data when constructing forecasts of future vari-

find that adaptive learning models are more successful than rational expectations models incapturing several quantitative properties of U.S macroeconomic data

Adam, Kuang and Marcet (2012) show that the introduction of constant-gain learning in

a small open economy can help account for recent cross-country patterns in house prices andcurrent account dynamics Granziera and Kozicki (2012) show that a simple Lucas-type assetpricing model with extrapolative expectations can match the run-up in U.S house prices from

that the introduction of endogenous switching between two types of simple forecasting rules in

a New Keynesian model can generate excess kurtosis in the simulated output gap, consistentwith U.S data

The basic structure of the model is similar to Iacoviello (2005) The economy is populated

by two types of households: patient (indexed by  = 1) and impatient (indexed by  = 2),

of mass 1 −  and , respectively Impatient households have a lower subjective discount

is assumed in the consumption goods sector Monetary policy follows a standard Taylor-typeinterest rate rule

2.1 Households

b

∞X

where the symbol b represents the subjective expectation of household type , conditional

on information available time  as explained more fully below Under rational expectations,b

distributions of the stochastic shocks, which are assumed known by the rational household The

level of consumption which the household takes into account when formulating its optimal

bud-get constraint:

2+ (2− 2−1) +2−1−1

2−1 is the borrower’s real debt at the end of period  − 1

New borrowing during period  is constrained in that impatient households may onlyborrow (principle and interest) up to a fraction of the expected value of their housing stock inperiod  + 1:



hb

subjective forecast of future variables that govern the collateral value and the real interest rateburden of the loan

The impatient household’s optimal choices are characterized by the following first-orderconditions:

1 9

Given that  2  1 it is straightforward to show that equation (3) holds with equality at the deterministic steady state As is common in the literature, we solve the model assuming that the constraint is binding in a neighbourhood around the steady state See, for example, Iacoviello (2005) and Iacoviello and Neri (2010).

receive the firm’s profits  and make one-period loans to borrowers The budget constraint

of the patient household is given by:

1+ + (1− 1−1) +1−1−1



−1+  (7)

households correspond to the aggregate loans of impatient households

The law of motion for physical capital is given by:

(    −1 )

The patient household’s optimal choices are characterized by the following first-order ditions:

2.2 Firms and Price Setting

Firms are owned by the patient households Hence, we assume that the subjective expectations

of firms are formulated in the same way as their owners

constant returns-to-scale technology:

where the inputs are a continuum of intermediate goods () and   1 is the constant

as given by the firms Cost minimization implies the following demand function for each

0 ()1−i1(1−)

In the wholesale sector, there is a continuum of firms indexed by  ∈ [0 1] and owned

by patient households Intermediate goods-producing firms act in a monopolistic market and

labor, according to the following constant returns-to-scale technology:

their differentiated goods following the Calvo (1983) model of staggered price setting Prices

price adjustment of non-optimizing firms Variables without time subscripts represent

cost-push shock

2.3 Monetary and Macroprudential Policy

In the baseline model, we assume that the central bank follows a simple Taylor-type rule ofthe form:

AR(1) policy shock

In the policy experiments, we consider the following generalized policy rule that allows for

a direct response to either credit growth or house price growth:

household debt, i.e., credit growth

In the aftermath of the global financial crisis, a wide variety of macroprudential policy

policy variables that appear in the collateral constraint For our first macroprudential policyexperiment, we allow the regulator to adjust the value of the parameter  in equation (3).Lower values of  imply tighter lending standards In the second macroprudential policyexperiment, we consider a generalized version of the borrowing constraint which takes theform

as being directed by the regulator As  increases, the regulator directs the lender to placemore emphasis on the borrower’s wage income when making a lending decision Whenever

loan-to-value ratio as in the baseline version of the constraint (3) In steady state, we therefore have

loan-to-value ratio is no longer constant but instead moves in the same direction as the ratio ofthe borrower’s wage income to housing collateral value Consequently, the equilibrium loan-to-value ratio will endogenously decline whenever the market value of housing collateral increasesfaster than the borrower’s wage income In this way, the generalized borrowing constraintacts like an automatic stabilizer to dampen fluctuations in household debt that are linked toexcessive movements in house prices

2.4 Expectations

Rational expectations are built on strong assumptions about households’ information In tual forecasting applications, real-time difficulties in observing stochastic shocks, together withempirical instabilities in the underlying shock distributions could lead to large and persistentforecast errors These ideas motivate consideration of a boundedly-rational forecasting algo-rithm, one that requires substantially less computational and informational resources A long

history in macroeconomics suggests the following adaptive (or error-correction) approach:

¤

simplicity, we assume that  is the same for both types of households

Equation (20) implies that the forecast at time  is an exponentially-weighted movingaverage of past observed values of the forecast object, where  governs the distribution ofweights assigned to past values–analogous to the gain parameter in the adaptive learningliterature When  = 1 households employ a simple random walk forecast By comparison,the “sticky-information” model of Mankiw and Reis (2002) implies that the forecast at time

 is based on an exponentially-weighted moving average of past rational forecasts A

For each of the model’s first order conditions, we nest the moving-average forecast rule (20)

which is a weighted-average of the two forecasts

b

where  can be interpreted as the fraction of households who employ the moving-averageforecast rule (20) For simplicity, we assume that  is the same for both types of households

who employ the moving-average forecast rule Although the parameters  and  influence thevolatility and persistence of the model variables, they do not affect the deterministic steadystate

Table 1 summarizes our choice of parameter values Some parameters are set to achievetarget values for steady-state variables while others are set to commonly-used values in the

literature.22 The time period in the model is one quarter The number of impatient householdsrelative to patient households is  = 09 so that patient households represent the top decile

of households in the model economy In the model, patient households own 100% of physicalcapital wealth The top decile of U.S households owns approximately 80% of financial wealthand about 70% of total wealth including real estate Our setup implies a Gini coefficientfor physical capital wealth of 0.90 The Gini coefficient for financial wealth in U.S data has

income decile in the model earns 40% of total income (including firm profits) in steady state,

The elasticity parameter  = 3333 is set to yield a steady-state price mark-up of about 3%

095 thus generating a strong desire for borrowing The investment adjustment cost parameter

 = 5 is in line with values typically estimated in DSGE models Capital depreciates at atypical quarterly rate of  = 0025 The habit formation parameter is  = 05 The labor

and impatient households, respectively Our calibration implies that the top income decile ofhouseholds derive a relatively higher per unit utility from housing services Together, thesevalues imply a steady-state ratio of total housing wealth to annualized GDP of 1.98 According

to Iacoviello (2010), the corresponding ratio in U.S data has ranged between 1.2 and 2.3 overthe period 1952 to 2008

values in the literature The interest rate responses to inflation and quarterly output are

The calibration of the forecast rule parameters  and  requires a more detailed description.Our aim is to magnify the volatility of house prices and household debt while maintaining pro-cyclical movement in both variables Figure 5 shows how different combinations of  and 

stable equilibrium does not exist for that particular combination of  and  The baselinecalibration of  = 030 and  = 035 delivers excess volatility and maintains pro-cyclicalmovement in house prices and household debt Even though only 30% of households in the

2 2 See, for example, Iacoviello and Neri (2010).

2 3

See Wolff (2006), Table 4.2, p 113.

2 4 Updated data through 2010 are available from Emmanuel Saez’s website: http://elsa.berkeley.edu/~saez/.

model employ a moving-average forecast rule, the presence of these agents influences the nature

effects of a direct interest rate response to financial variables Very high values for theseparameters can sometimes lead to instability of the steady state The constant loan-to-valueratio in the baseline model is  = 07 This is consistent with the long-run average loan-to-

(19), we set  = 05 which requires the lender to place a substantial weight on the borrowers

ratio as in the baseline model with  = 0

In the sensitivity analysis, we examine the volatility effects of varying the key policy

[02 10]  and  ∈ [0 10] 

In this section, we show that the hybrid expectations model generates excess volatility inasset prices and household debt while at the same time delivering co-movement between houseprices, household debt, and real output In this way, the model is better able to match thepatterns observed in many developed countries over the past decade

Figure 6 depicts simulated time series for the house price, household debt, the price of

percent deviations from steady state values without applying any filter The figure shows thatthe hybrid expectations model serves to magnify the volatility of most model variables This isnot surprising given that the moving-average forecast rule (20) embeds a unit root assumption.This is most obvious when  = 1 but is also true when 0    1 because the weights on laggedvariables sum to unity Due to the self-referential nature of the equilibrium conditions, the

2 5

Levine et al (2012) employ a specification for expectations that is very similar to our equations (20) and (21) However, their DSGE model omits house prices and household debt They estimate the fraction of backward-looking agents ( in our model) in the range of 0.65 to 0.83 with a moving-average forecast parameter ( in our model) in the range of 0.1 to 0.4.

2 6

We thank Bill Emmons of the Federal Reserve Bank of St Louis for kindly providing this data, which are plotted in Figure 4.

2 7 A simple example with  = 1 illustrates the point Suppose that the Phillips curve is given by   =

     +1 +    where   follows an AR(1) process with persistence  and     +1 =    +1 + (1 − )    +1  When    +1 =    the equilibrium law of motion is   =    [1 −  −  (1 − )], which implies   (  ) =

  (  )  [1 −  −  (1 − )]2When   1 both   (  ) and   (   +1 ) are increasing in the fraction

of agents  who employ a random walk forecast.

The use of moving-average forecast rules by a subset of agents also influences the nature of thefully-rational forecast rules employed by the remaining agents Both of these channels serve

to magnify volatility

Table 2 compares volatilities under rational expectations ( = 0) to those under hybridexpectations where a fraction  = 030 of agents employ moving-average forecast rules Excessvolatility is greatest for the household debt series which is magnified by a factor 2.07 Thevolatility of house prices is magnified by a factor of 1.77 House price volatility is magnified byless than debt volatility because the patient-lender households in the model do not use debt forthe purchase of housing services The volatility of labor hours is magnified by a factor of 1.92whereas output volatility is magnified by a factor of 1.36 Stock price volatility is magnified

by a factor of 1.30 The volatilities of the other variables are also magnified, but in a lessdramatic way Consumption volatility is magnified by a factor 1.12

Given the calibration of the shocks, the hybrid expectations model approximately matchesthe standard deviations of log-linearly detrended U.S real house prices, real household debtper capita, and real GDP per capita over the period 1965 to 2009 A comparison of the modelsimulations shown in Figure 6 with the U.S data shown earlier in Figure 1 confirms that themodel fluctuations for these variables are similar in amplitude to those in the detrended data.Another salient feature of the recent U.S data, reproduced by the hybrid expectations model,

is the co-movement of GDP, house prices, and household debt Our simulations mimic theevidence that in a period of economic expansion, a house price boom is accompanied by anincrease in household debt, as the collateral constraint allows both to move up simultaneously.Table 3 shows that the persistence of most model variables is higher under hybrid ex-pectations The autocorrelation coefficient for house prices goes from 0.90 under rationalexpectations to 0.97 under hybrid expectations, whereas the autocorrelation coefficient forhousehold debt goes from 0.79 to 0.94 The increased persistence improves the model’s ability

to produce large swings in house prices and household debt, as was observed in many developedcountries over the past decade

Figures 7 through 9 plot impulse response functions In the case of all three shocks,the resulting fluctuations in the hybrid expectations model tend to be more pronounced andlonger lasting The overreaction of house prices and stock prices to fundamental shocks in thehybrid expectations model is consistent with historical interpretations of bubbles As noted

by Greenspan (2002), “Bubbles are often precipitated by perceptions of real improvements inthe productivity and underlying profitability of the corporate economy But as history attests,investors then too often exaggerate the extent of the improvement in economic fundamentals.”

As noted in the introduction, countries with the largest increases in household leveragetended to experience the fastest run-ups in house prices from 1997 to 2007 The same countriestended to experience the most severe declines in consumption once house prices started falling

The hybrid expectations model delivers the result that excess volatility in house prices andhousehold debt also gives rise to excess volatility in consumption Hence, central bank efforts

to dampen boom-bust cycles in housing and credit may yield significant welfare benefits fromsmoother consumption

Central bank loss functions are often modeled as a weighted-sum of squared deviations

of inflation and output from targets In our model, such a loss function is equivalent to

a weighted-sum of the unconditional variances of inflation and output since the target (orsteady-state) values of both variables equal zero The results shown in Table 2 imply a higherloss function realization under hybrid expectations As discussed further in the next section,

a concern for financial stability might be reflected in an expanded loss function that takes intoaccount the variance of household debt In this case, the high volatility of household debtobserved under hybrid expectations would imply a higher loss function realization and hence

a stronger motive for central bank stabilization policy

In this section, we evaluate various policy actions that might be used to dampen excess ity in the model economy We first examine the merits of a direct response to either houseprice growth or household debt growth in the central bank’s interest rate rule Next, we an-alyze the use of two macroprudential policy tools that affect the borrowing constraint, i.e.,

volatil-a permvolatil-anent reduction in the lovolatil-an-to-vvolatil-alue rvolatil-atio volatil-and volatil-a policy thvolatil-at directs lenders to plvolatil-aceincreased emphasis on the borrower’s wage income in determining how much they can borrow

5.1 Interest Rate Response to House Price Growth or Credit Growth

The generalized interest rate rule (18) allows for a direct response to either house price growthcredit growth As an illustrative case, Table 3 shows the results when the central bank responds

The top panel of Table 4 shows that under rational expectations, responding to house pricesdoes not yield any stabilization benefits for output but the volatility of labor hours is magnified

by a factor of 1.29 (relative to the no-response version of the same model) The standarddeviation of inflation is somewhat magnified with a volatility ratio of 1.06 These results are

in line with Iacoviello (2005) who finds little or no stabilization benefits for an interest rateresponse to the level of house prices in a rational expectations model The largest stabilizationeffect under rational expectations is achieved with household debt which exhibits a volatilityratio 0.77 Consumption volatility is reduced with a ratio 0.95 Under hybrid expectations,responding to house price growth yields qualitatively similar results However, the undesirablemagnification of inflation volatility is now quantitatively much larger–exhibiting a volatility

ratio of 1.21 The policy under hybrid expectations delivers some stabilization benefits forhousehold debt (volatility ratio of 0.93), but consumption volatility is little changed (volatilityratio of 0.99) and labor hours volatility is magnified (volatility ratio of 1.15).

The bottom panel of Table 4 shows the results for an interest rate response to credit growth.Under rational expectations, the results are broadly similar to an interest rate response tohouse price growth However, under hybrid expectations, responding to credit growth nowperforms poorly Specifically, inflation volatility is magnified by a factor of 1.83 and there is

no compensating reduction in the volatility of household debt On the contrary, debt volatility

is slightly magnified by a factor of 1.03 The volatility of labor hours is magnified by a factor

of 1.06 These results demonstrate that the stabilization benefits of a particular monetarypolicy can be influenced by the nature of agents’ expectations Under rational expectations,the impatient households understand that an increase in borrowing will contribute to higher

serves to dampen fluctuations in household debt But under hybrid expectations, this channelbecomes less effective because a subset of borrowers construct forecasts using a moving-average

of past values

vary from a low 0 to a high of 0.4 Both policy rules end up magnifying the volatility ofoutput, labor hours, and inflation, with the undesirable effect on inflation being more severewhen responding to credit growth In the lower right panel of the figure, we plot the realizedvalues of two illustrative loss functions that are intended to represent plausible stabilizationgoals of a central bank Loss function 1 is a commonly-used specification consisting of anequal-weighted sum of the unconditional variances of inflation and output Loss function 2includes an additional term not present in loss function 1, namely, the unconditional variance

of household debt which is assigned a relative weight of 0.25 We interpret the additional term

as reflecting the central bank’s concern for financial stability Here, we link the concern forfinancial stability to a variable that measures household leverage whereas Woodford (2011)links this concern to a variable that measures financial sector leverage

Figures 10 and 11 show that responding to either house price growth or credit growth isdetrimental from the standpoint of loss function 1 However, in light of the severe economicfallout from the recent financial crisis, views regarding the central bank’s role in ensuringfinancial stability appear to be shifting From the standpoint of loss function 2, an interestrate response to house price growth achieves some success in reducing the loss, provided

credit growth remains detrimental under loss function 2 because the policy does not stabilizefluctuations in household debt

As a caveat to the above results, we acknowledge that the parameters of the Taylor-type

interest rate rule (18) have not been optimized to minimize the value of any loss function.Moreover, unlike an optimal simple rule, the fully-optimal monetary policy should respond toall state variables in the model In the case of hybrid expectations, the lagged expectation

of backward-looking agents (i.e., the lagged moving average of the forecast variable) wouldrepresent an additional state variable that should appear in the central bank’s fully-optimalpolicy rule While an exploration of optimal monetary policy is beyond the scope of this paper,such an exploration might identify some stabilization benefits to responding to either houseprice growth or credit growth

5.2 Tightening of Lending Standards: Decrease LTV

The top panel of Table 5 shows the results for a macroprudential policy that permanentlytightens lending standards by reducing the maximum loan-to-value ratio  in equation (3)from 0.7 to 0.5 Under both rational and hybrid expectations, the policy succeeds in reducingthe volatility of household debt, but the volatility of most other variables, including output,labor hours, and inflation are slightly magnified

Figure 12 plots the results for hybrid expectations when we allow  to vary from a low 0.2

to a high of 1.0 The figure shows that higher values of  (implying looser lending standards)reduce the volatility of output, labor hours, inflation, and consumption over a middle range ofloan-to-value ratios However, as  approaches 1.0, the volatilities of inflation and consumptionstart increasing again

The volatility patterns shown in Figure 12 illustrate a complicated policy trade-off Onthe one hand, a tightening of lending standards can stabilize household debt and therebyhelp promote financial stability But on the other hand, permanently restricting access toborrowed money will impair the ability of impatient households to smooth their consumption,thus magnifying the volatility of aggregate consumption, as well as output, aggregate laborhours, and inflation

In the lower right panel of Figure 12, we see that a decrease in  starting from 0.7 isdetrimental from the standpoint of loss function 1 which only considers output and inflation.However, the same policy is beneficial from the standpoint of loss function 2 which takes intoaccount financial stability via fluctuations in household debt Under these circumstances, adecision by regulators to tighten lending standards could be met with opposition from thosewho do not share the regulator’s concern for financial stability

5.3 Wage Income in the Borrowing Constraint

The bottom panel of Table 5 shows the results for a macroprudential policy that requireslenders to place a substantial emphasis on the borrower’s wage income in the borrowing con-

straint Specifically, we set  = 05 in equation (19) with b = 1072 so as to leave thesteady-state loan-to-value ratio unchanged from the baseline model with  = 0

Under both expectations regimes, the policy succeeds in reducing the volatility of householddebt Under rational expectations, the volatility of household debt is reduced by a factor of0.86 Under hybrid expectations, debt volatility is reduced by a factor 0.68 The volatilityeffects on the other variables are generally quite small, but for the most part, volatilities arereduced under hybrid expectations

Figure 13 plots the results for hybrid expectations when we allow  to vary from a low ofzero (representing a pure loan-to-value constraint) to a high of 1.0 (representing a pure loan-to-income constraint) As  increases, the policy achieves small reductions in the volatilities

of output, labor hours, inflation, and consumption Notably, the policy avoids the undesirablemagnification of inflation volatility that was observed in the two interest rate policy experi-ments In this sense, the present policy can be viewed as superior simply because it avoidsdoing harm In the lower right panel of the figure, we see that an increase in  achieves smallstabilization benefits from the standpoint of loss function 1, but much larger benefits from thestandpoint of loss function 2

Figure 14 shows that the generalized borrowing constraint with  = 05 induces nous countercyclicality of the loan-to-value ratio In this way, the policy serves as an “auto-matic stabilizer” for household debt The intuition for this result is straightforward Dividing

where the left-side variable is the equilibrium loan-to-value ratio plotted in Figure 14 When

 = 0 the left-side variable is constant However when   0 the left-side variable will move

b

i

stronger under hybrid expectations

Housing values in the U.S rose faster than wage income during the boom years of themid-2000s Unfortunately, lenders did not react by tightening lending standards as called for

by a constraint such as (22) On the contrary, lending standards deteriorated as the boomprogressed Rather than placing a substantial weight on the borrower’s wage income in theunderwriting decision, lenders increasingly approved mortgages with little or no documenta-

2 8

According to the U.S Financial Crisis Inquiry Commission (2011), p 165, “Overall, by 2006, no-doc or low-doc loans made up 27% of all mortgages originated.”

the stabilization benefits of countercyclical loan-to-value rules in rational expectations els While it may be possible to successfully implement such state-contingent rules within

mod-a regulmod-atory frmod-amework, it seems much emod-asier mod-and more trmod-anspmod-arent for regulmod-ators to simplymandate a substantial emphasis on the borrower’s wage income in the lending decision

There are many examples in history of asset prices exhibiting sustained run-ups that aredifficult to justify on the basis of economic fundamentals The typical transitory nature ofthese run-ups should perhaps be viewed as a long-run victory for fundamental asset pricingtheory Still, it remains a challenge for fundamental theory to explain the ever-present volatility

of asset prices within a framework of efficient markets and fully-rational agents

This paper showed that the introduction of a subset of agents who employ simple average forecast rules can significantly magnify the volatility of house prices and householddebt versus an otherwise similar model with fully-rational agents A wide variety of empiricalevidence supports the idea that expectations are often less than fully-rational One obviousexample can be found in survey-based measures of U.S inflation expectations which are well-captured by a moving average of past inflation rates A moving-average forecast rule can also

moving-be justified as an approximation to a standard Kalman filter algorithm in which the forecastvariable is subject to both permanent and temporary shocks

The extensive harm caused by the global financial crisis raises the question of whetherpolicymakers could have done more to prevent the buildup of dangerous financial imbalances,particularly in the household sector The U.S Financial Crisis Inquiry Commission (2011)concluded, “Despite the expressed view of many on Wall Street and in Washington that thecrisis could not have been foreseen or avoided, there were warning signs The tragedy wasthat they were ignored or discounted There was an explosion in risky subprime lending andsecuritization, an unsustainable rise in housing prices, widespread reports of egregious andpredatory lending practices, dramatic increases in household mortgage debt among manyother red flags Yet there was pervasive permissiveness; little meaningful action was taken

to quell the threats in a timely manner.” In the aftermath of the crisis, there remain tant unresolved questions about whether regulators should attempt to lean against suspectedbubbles and if so, what policy instruments should be used to do so

impor-This paper evaluated the performance of some monetary and macroprudential policy tools

as a way of dampening excess volatility in a DSGE model with housing While no policytool was perfect, some performed better than others A direct response to either house pricegrowth or credit growth in the central bank’s interest rate rule had the serious drawback ofsubstantially magnifying the volatility of inflation A tightening of lending standards, in the